where \(F_{\mu \nu } =\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu }\)  is the field strength tensor. The Ricci tensor is given by [1]}
\(R_{\mu \nu } =\frac{1}{2}( \partial _{\sigma }\partial _{\nu }h^{\sigma }_{\,\,\,\mu } + \partial _{\sigma }\partial _{\mu }h^{\sigma }_{\,\,\,\nu } -\partial _{\mu }\partial _{\nu }h - \Box h_{\mu \nu } ) \,.\) 
